Facebook said the suspect did go live on the social media website at one point during the day, but not during the killing. Chief Williams also said Stephens' family was also urging him to turn himself in to police.
"Any problems he is having, we can have a conversation", Williams said.
He then tells the friend he has killed 13 people, "and I'm about to keep killing until they catch me".
Mr Stephens should be considered armed and unsafe, police said.
A Facebook Live video (which has since been taken down) started the Cleveland Police Department on a manhunt on Easter Sunday, April 16.
WKYC has edited the clip below from the original video posted on Facebook, but some users may still may find the edited footage hard to watch.
Stephens also claimed to have committed multiple homicides, according to police.
In a statement, a Facebook spokesperson said the shooting was a "horrific crime". Police said Stephens is armed and risky and should not be approached. They said the suspect was last seen south of Interstate-90 in the area of East 93rd.
Police said the suspect made claims of killing other people in addition the Facebook Live murder, but said they have not yet verified those claims.
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Horrifying video footage has emerged on social media apparently showing a man walking up to someone he doesn't know and shooting him dead.
Williams said Stephens may be driving a newer model white Ford Fusion, possibly with a temporary license plate.
Stephens, a case manager with Beech Brook, a children's behavioral health agency, had recently been working with young adults, a Beech Brook official told BuzzFeed News.
Stephens is an employee at Beech Brook, a children's behavioral health center in OH, a company spokesperson told ABC News. Anyone with information is asked to call 911.
The victim's son, Robert Godwin Jr., told Cleveland.com that he can't bring himself to watch the video.
He added: "I'm the good guy".
City authorities identified the homicide victim as Robert Godwin, 74.
Stephens then drove his auto away from the scene, and spoke calmly to the camera for several minutes as the live stream continued.
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